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SELECTIVE GROUPOIDS AND FRAMEWORKS INDUCED BY FUZZY SUBSETS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 11، دوره 14، شماره 3، شهریور 2017، صفحه 151-160 اصل مقاله (350.48 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3261 | ||
| نویسندگان | ||
| Young Hee Kim1؛ Hee Sik Kim* 2؛ J. Neggers3 | ||
| 1Department of Mathematics, Chungbuk National University, Cheongju, 28644, Korea | ||
| 2Research Institute for Natural Sci., Department of Mathematics, Hanyang University, Seoul, 04763, Korea | ||
| 3Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U. S. A. | ||
| چکیده | ||
| In this paper, we show that every selective groupoid induced by a fuzzy subset is a pogroupoid, and we discuss several properties in quasi ordered sets by introducing the notion of a framework. | ||
| کلیدواژهها | ||
| Fuzzy subset؛ $d/BCK$-algebra؛ Framework؛ Selective groupoid؛ Pogroupoid؛ Poset | ||
| مراجع | ||
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[1] R. K. Bandaru, K. P. Shum and N. Ra , Fuzzy ideals of implication groupoids, Italian J. Pure and Appl. Math., 34 (2015), 277{290. [2] G. Gratzer, General lattice theory, Springer, New York, 1978. [3] J. S. Han, H. S. Kim and J. Neggers, Strong and ordinary d-algebras, J. Mult.-Valued Logic & Soft Computing, 16 (2010), 331{339. [4] D. Kelly and I. Rival, Planar lattices, Canad. J. Math., 27 (1975), 636{665. [5] M. Khan, M. Shakeel, M. Gulistan and S. Rashid, Generalized fuzzy bi-ideals of order right modular groupoids, Int. J. Algebra and Statistics, 4 (2015), 46{56. [6] H. S. Kim and J. Neggers, The semigroups of binary systems and some perspectives, Bull. Korean Math. Soc., 45 (2008), 651{661. [7] J. Neggers, Partially ordered sets and groupoids, Kyungpook Math. J., 16 (1976), 7{20. [8] J. Neggers and H. S. Kim, Modular posets and semigroups, Semigroup Forum, 53 (1996), 57{62. [9] J. Neggers and H. S. Kim, On d-algebras, Math. Slovaca, 49 (1999), 19{26. [10] J. Neggers and H. S. Kim, Algebras associated with posets, Demonstratio Math., 34 (2001), 13{23. [11] J. Neggers and H. S. Kim, Fuzzy posets on sets, Fuzzy Sets and Sys., 117 (2001), 391{402. [12] J. Neggers and H. S. Kim, Fuzzy pogroupoids, Information Sci., 175 (2005), 108{119. [13] S. J. Shin, H. S. Kim and J. Neggers, On Abelian and related fuzzy subsets of groupoids, The Scienti c World J., Article ID 476057, 2013 (2013), 5 pages. [14] S. J. Shin, H. S. Kim and J. Neggers, The intersection between fuzzy subsets and groupoids, The Scienti c World J., Article ID 246285, 2014 (2014), 6 pages. [15] L. Zadeh, Fuzzy Sets, Inform. and Control, 8 (1965), 338{353. | ||
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